Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere     

Toshio Fukushima 《Journal of Geodesy》2018,92(2):123-130

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the \(4 \pi \) fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as \(2^{30}\,{\approx }\,10^9\). The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.  相似文献   

A method solving kepler's equation without transcendental function evaluations     

Toshio Fukushima 《Celestial Mechanics and Dynamical Astronomy》1996,66(3):309-319

We developed two approximations of the Newton-Raphson method. The one is a sort of discretization, namely to search an approximate solution on pre-specified grid points. The other is a Taylor series expansion. A combination of these was applied to solving Kepler's equation for the elliptic case. The resulting method requires no evaluation of transcendental functions. Numerical measurements showed that, in the case of Intel Pentium processor, the new method is three times as fast as the original Newton-Raphson method. Also it is more than 2.5 times as fast as Halley's method, Nijenhuis's method, and others.  相似文献   

Shock metamorphism on the moon     

Yasunori Miura  Toshio Kato 《Celestial Mechanics and Dynamical Astronomy》1992,54(1-3):245-248

Shock metamorphism of the lunar samples is discussed. All types of lunar glasses formed by various-size collision-type impact are found as impact glass, ropy glass and agglutinates. The agglutinates bonded by crystal and glassy materials contain hydrogen and helium from the solar wind components. Lunar shocked minerals of plagioclase and silica show anomalous compositions and densities. There are typical two formation processes on planetary materials formed by shock events; that is (1) shocked quartz formed by silica-rich target rocks (esp. on evolved planets of the Earth and Mars), and (2) shocked silica with minor Al contents formed from plagioclase-rich primordial crusts of the Moon. The both shocked silica grows to coarse-grain normal crystals after high-temperature metamorphism which cannot distinguish the original main formation event of impact process.  相似文献   

Verification of Carbon Sink Assessment: Can We Exclude Natural Sinks?   总被引：1，自引：0，他引：1  

Georgii?AlexandrovEmail author  Yoshiki?Yamagata 《Climatic change》2004,67(2-3):437-447

Any human-induced terrestrial sink is susceptible to the effects of elevated atmospheric CO₂ concentration, nitrogen deposition, climate variability and other natural or indirect human-induced factors. It has been suggested in climate negotiations that the effects of these factors should be excluded from estimates of carbon sequestration used to meet the emission reduction commitments under the Kyoto Protocol. This paper focuses on the methodologies for factoring out the effects of atmospheric and climate variability/change. We estimate the relative magnitude of the non-human induced effects by using two biosphere models and discuss possibilities for narrowing estimate uncertainty.  相似文献   

IOD and ENSO impacts on the extreme stream-flows of Citarum river in Indonesia     

Netrananda Sahu  Swadhin K. Behera  Yosuke Yamashiki  Kaoru Takara  Toshio Yamagata 《Climate Dynamics》2012,39(7-8):1673-1680

Extreme stream-flow events of Citarum River are derived from the daily stream-flows at the Nanjung gauge station. Those events are identified based on their persistently extreme flows for 6 or more days during boreal fall when the seasonal mean stream-flow starts peaking-up from the lowest seasonal flows of June–August. Most of the extreme events of high-streamflows were related to La Ni?a conditions of tropical Pacific. A few of them were also associated with the negative phases of IOD and the newly identified El Ni?o Modoki. Unlike the cases of extreme high streamflows, extreme low streamflow events are seen to be associated with the positive IODs. Nevertheless, it was also found that the low-stream-flow events related to positive IOD events were also associated with El Ni?o events except for one independent event of 1977. Because the occurrence season coincides the peak season of IOD, not only the picked extreme events are seen to fall under the IOD seasons but also there exists a statistically significant correlation of 0.51 between the seasonal IOD index and the seasonal streamflows. There also exists a significant lag correlation when IOD of June–August season leads the streamflows of September–November. A significant but lower correlation coefficient (0.39) is also found between the seasonal streamflow and El Ni?o for September–November season only.  相似文献   

Probabilistic prediction of Indian summer monsoon rainfall using global climate models   总被引：1，自引：0，他引：1  

Makarand A. Kulkarni  Nachiketa Acharya  Sarat C. Kar  U. C. Mohanty  Michael K. Tippett  Andrew W. Robertson  Jing-Jia Luo  Toshio Yamagata 《Theoretical and Applied Climatology》2012,107(3-4):441-450

Probabilistic seasonal predictions of rainfall that incorporate proper uncertainties are essential for climate risk management. In this study, three different multi-model ensemble (MME) approaches are used to generate probabilistic seasonal hindcasts of the Indian summer monsoon rainfall based on a set of eight global climate models for the 1982–2009 period. The three MME approaches differ in their calculation of spread of the forecast distribution, treated as a Gaussian, while all three use the simple multi-model subdivision average to define the mean of the forecast distribution. The first two approaches use the within-ensemble spread and error residuals of ensemble mean hindcasts, respectively, to compute the variance of the forecast distribution. The third approach makes use of the correlation between the ensemble mean hindcasts and the observations to define the spread using a signal-to-noise ratio. Hindcasts are verified against high-resolution gridded rainfall data from India Meteorological Department in terms of meteorological subdivision spatial averages. The use of correlation for calculating the spread provides better skill than the other two methods in terms of rank probability skill score. In order to further improve the skill, an additional method has been used to generate multi-model probabilistic predictions based on simple averaging of tercile category probabilities from individual models. It is also noted that when such a method is used, skill of probabilistic forecasts is improved as compared with using the multi-model ensemble mean to define the mean of the forecast distribution and then probabilities are estimated. However, skill of the probabilistic predictions of the Indian monsoon rainfall is too low.  相似文献   

The role of the intra-daily SST variability in the Indian monsoon variability and monsoon-ENSO–IOD relationships in a global coupled model     

Pascal Terray  Kakitha Kamala  Sébastien Masson  Gurvan Madec  A. K. Sahai  Jing-Jia Luo  Toshio Yamagata 《Climate Dynamics》2012,39(3-4):729-754

The impact of diurnal SST coupling and vertical oceanic resolution on the simulation of the Indian Summer Monsoon (ISM) and its relationships with El Ni?o-Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) events are studied through the analysis of four integrations of a high resolution Coupled General Circulation Model (CGCM), but with different configurations. The only differences between the four integrations are the frequency of coupling between the ocean and atmosphere for the Sea Surface Temperature (SST) parameter (2 vs. 24?h coupling) and/or the vertical oceanic resolution (31 vs. 301 levels) in the CGCM. Although the summer mean tropical climate is reasonably well captured with all the configurations of the CGCM and is not significantly modified by changing the frequency of SST coupling from once to twelve per day, the ISM–ENSO teleconnections are rather poorly simulated in the two simulations in which SST is exchanged only once per day, independently of the vertical oceanic resolution used in the CGCM. Surprisingly, when 2?h SST coupling is implemented in the CGCM, the ISM–ENSO teleconnection is better simulated, particularly, the complex lead-lag relationships between the two phenomena, in which a weak ISM occurs during the developing phase of an El Ni?o event in the Pacific, are closely resembling the observed ones. Evidence is presented to show that these improvements are related to changes in the characteristics of the model’s El Ni?o which has a more realistic evolution in its developing and decaying phases, a stronger amplitude and a shift to lower frequencies when a 2-hourly SST coupling strategy is implemented without any significant changes in the basic state of the CGCM. As a consequence of these improvements in ENSO variability, the lead relationships between Indo-Pacific SSTs and ISM rainfall resemble the observed patterns more closely, the ISM–ENSO teleconnection is strengthened during boreal summer and ISM rainfall power spectrum is in better agreement with observations. On the other hand, the ISM–IOD teleconnection is sensitive to both SST coupling frequency and the vertical oceanic resolution, but increasing the vertical oceanic resolution is degrading the ISM–IOD teleconnection in the CGCM. These results highlight the need of a proper assessment of both temporal scale interactions and coupling strategies in order to improve current CGCMs. These results, which must be confirmed with other CGCMs, have also important implications for dynamical seasonal prediction systems or climate change projections of the monsoon.  相似文献   

Impact of intra-daily SST variability on ENSO characteristics in a coupled model   总被引：1，自引：1，他引：0  

Sébastien Masson  Pascal Terray  Gurvan Madec  Jing-Jia Luo  Toshio Yamagata  Keiko Takahashi 《Climate Dynamics》2012,39(3-4):681-707

This paper explores the impact of intra-daily Sea Surface Temperature (SST) variability on the tropical large-scale climate variability and differentiates it from the response of the system to the forcing of the solar diurnal cycle. Our methodology is based on a set of numerical experiments based on a fully global coupled ocean–atmosphere general circulation in which we alter (1) the frequency at which the atmosphere sees the SST variations and (2) the amplitude of the SST diurnal cycle. Our results highlight the complexity of the scale interactions existing between the intra-daily and inter-annual variability of the tropical climate system. Neglecting the SST intra-daily variability results, in our CGCM, to a systematic decrease of 15% of El Ni?o—Southern Oscillation (ENSO) amplitude. Furthermore, ENSO frequency and skewness are also significantly modified and are in better agreement with observations when SST intra-daily variability is directly taken into account in the coupling interface of our CGCM. These significant modifications of the SST interannual variability are not associated with any remarkable changes in the mean state or the seasonal variability. They can therefore not be explained by a rectification of the mean state as usually advocated in recent studies focusing on the diurnal cycle and its impact. Furthermore, we demonstrate that SST high frequency coupling is systematically associated with a strengthening of the air-sea feedbacks involved in ENSO physics: SST/sea level pressure (or Bjerknes) feedback, zonal wind/heat content (or Wyrtki) feedback, but also negative surface heat flux feedbacks. In our model, nearly all these results (excepted for SST skewness) are independent of the amplitude of the SST diurnal cycle suggesting that the systematic deterioration of the air-sea coupling by a daily exchange of SST information is cascading toward the major mode of tropical variability, i.e. ENSO.  相似文献   

Advance and prospectus of seasonal prediction: assessment of the APCC/CliPAS 14-model ensemble retrospective seasonal prediction (1980–2004)     

Bin Wang  June-Yi Lee  In-Sik Kang  J. Shukla  C.-K. Park  A. Kumar  J. Schemm  S. Cocke  J.-S. Kug  J.-J. Luo  T. Zhou  B. Wang  X. Fu  W.-T. Yun  O. Alves  E. K. Jin  J. Kinter  B. Kirtman  T. Krishnamurti  N. C. Lau  W. Lau  P. Liu  P. Pegion  T. Rosati  S. Schubert  W. Stern  M. Suarez  T. Yamagata 《Climate Dynamics》2009,33(1):93-117

We assessed current status of multi-model ensemble (MME) deterministic and probabilistic seasonal prediction based on 25-year (1980–2004) retrospective forecasts performed by 14 climate model systems (7 one-tier and 7 two-tier systems) that participate in the Climate Prediction and its Application to Society (CliPAS) project sponsored by the Asian-Pacific Economic Cooperation Climate Center (APCC). We also evaluated seven DEMETER models’ MME for the period of 1981–2001 for comparison. Based on the assessment, future direction for improvement of seasonal prediction is discussed. We found that two measures of probabilistic forecast skill, the Brier Skill Score (BSS) and Area under the Relative Operating Characteristic curve (AROC), display similar spatial patterns as those represented by temporal correlation coefficient (TCC) score of deterministic MME forecast. A TCC score of 0.6 corresponds approximately to a BSS of 0.1 and an AROC of 0.7 and beyond these critical threshold values, they are almost linearly correlated. The MME method is demonstrated to be a valuable approach for reducing errors and quantifying forecast uncertainty due to model formulation. The MME prediction skill is substantially better than the averaged skill of all individual models. For instance, the TCC score of CliPAS one-tier MME forecast of Niño 3.4 index at a 6-month lead initiated from 1 May is 0.77, which is significantly higher than the corresponding averaged skill of seven individual coupled models (0.63). The MME made by using 14 coupled models from both DEMETER and CliPAS shows an even higher TCC score of 0.87. Effectiveness of MME depends on the averaged skill of individual models and their mutual independency. For probabilistic forecast the CliPAS MME gains considerable skill from increased forecast reliability as the number of model being used increases; the forecast resolution also increases for 2 m temperature but slightly decreases for precipitation. Equatorial Sea Surface Temperature (SST) anomalies are primary sources of atmospheric climate variability worldwide. The MME 1-month lead hindcast can predict, with high fidelity, the spatial–temporal structures of the first two leading empirical orthogonal modes of the equatorial SST anomalies for both boreal summer (JJA) and winter (DJF), which account for about 80–90% of the total variance. The major bias is a westward shift of SST anomaly between the dateline and 120°E, which may potentially degrade global teleconnection associated with it. The TCC score for SST predictions over the equatorial eastern Indian Ocean reaches about 0.68 with a 6-month lead forecast. However, the TCC score for Indian Ocean Dipole (IOD) index drops below 0.40 at a 3-month lead for both the May and November initial conditions due to the prediction barriers across July, and January, respectively. The MME prediction skills are well correlated with the amplitude of Niño 3.4 SST variation. The forecasts for 2 m air temperature are better in El Niño years than in La Niña years. The precipitation and circulation are predicted better in ENSO-decaying JJA than in ENSO-developing JJA. There is virtually no skill in ENSO-neutral years. Continuing improvement of the one-tier climate model’s slow coupled dynamics in reproducing realistic amplitude, spatial patterns, and temporal evolution of ENSO cycle is a key for long-lead seasonal forecast. Forecast of monsoon precipitation remains a major challenge. The seasonal rainfall predictions over land and during local summer have little skill, especially over tropical Africa. The differences in forecast skills over land areas between the CliPAS and DEMETER MMEs indicate potentials for further improvement of prediction over land. There is an urgent need to assess impacts of land surface initialization on the skill of seasonal and monthly forecast using a multi-model framework.  相似文献   

Erratum to: Effect of the variation in the lower tropospheric temperature on the wind onset of the Indian summer monsoon   总被引：1，自引：0，他引：1  

Kenji Taniguchi  Devaraj Rajan  Toshio Koike 《Meteorology and Atmospheric Physics》2010,106(3-4):227-227

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